Functions, polynomials and the binomial
Work with polynomials, use the factor theorem, and expand brackets raised to any power.
7 chapters planned
Level 5
Start here if you can already: Read a textbook. Use functions and graphs. If a book feels hard, the one below it in the same topic is a good step back.
No book in this level is written yet. Each card below shows its plan, which a teacher can already use.
Mathematics
8 books planned. Each one shows its plan.
Exponentials and logarithms
Use the number e and logarithms to model growth and to solve equations where the unknown is a power.
7 chapters planned
Trigonometric functions
Measure angles in radians, solve trig equations, and prove identities.
8 chapters planned
Differentiation
Find how fast things change, and use it to find the highest and lowest points of curves.
8 chapters planned
Vectors and matrices
Use vectors for position and direction, and matrices to move shapes and solve equations.
8 chapters planned
Probability distributions and inference
Model random events with distributions, and test claims using samples.
8 chapters planned
Proof, sequences and series
Learn to prove things for certain, and work with sequences and their sums.
8 chapters planned
Science
15 books planned. Each one shows its plan.
Molecules and cells
Life runs on a few kinds of molecule working together inside cells.
8 chapters planned
Genetics and evolution
Genes pass on in patterns we can predict, and populations change as their genes change.
8 chapters planned
Photosynthesis, respiration and ecosystems
Plants capture energy from sunlight, cells release it, and ecosystems pass it along.
8 chapters planned
Physiology
The organs of the body work together to exchange gases, move blood, fight disease and keep conditions steady.
8 chapters planned
Bonding and structure
The way atoms share or pass on electrons sets the shape and properties of every substance.
8 chapters planned
Energetics, rates and equilibrium
Energy changes, reaction speeds and equilibrium tell us how far and how fast a reaction goes.
8 chapters planned
Acids, redox and the periodic table
Acids, electron transfer and patterns in the periodic table explain a great deal of chemistry.
8 chapters planned
Organic chemistry
Carbon forms millions of compounds, and a few patterns explain how they react.
8 chapters planned
Waves
Waves add up, bend and spread, and this explains music, rainbows and the light from stars.
8 chapters planned
Quanta, nuclei and particles
Light comes in packets, matter acts like waves, and the nucleus holds huge amounts of energy.
8 chapters planned
Thermal physics
Thermal physics links the motion of tiny particles to temperature, pressure and heat.
7 chapters planned
Fields
Gravity, electric charge and magnetism all act at a distance through fields that follow similar rules.
8 chapters planned
Electric circuits and capacitors
Circuits follow rules about charge and energy, and capacitors store charge for later.
8 chapters planned
Astrophysics and cosmology
Physics lets us measure the stars and trace the universe back to its beginning.
8 chapters planned
Practice papers
One paper for each class and subject, drawn from the books of that class, with a mark scheme. None is ready yet. They are being written now.
Mathematics
Science
Mathematics
Science